MOSCOW  Tens of thousands of Russians jammed a Moscow avenue to demand free elections and an end to Prime Minister Vladimir Putin's 12-year rule, in the largest show of public outrage since the protests 20 years ago that brought down the Soviet Union. Gone was the political apathy of recent years as many shouted "We are the Power!"

Saturday's demonstration, bigger and better organized than a similar one two weeks ago, and smaller rallies across the country encouraged opposition leaders hoping to sustain a protest movement ignited by a fraud-tainted parliamentary election on Dec. 4.

The enthusiasm also cheered Mikhail Gorbachev, the last Soviet leader who closed down the Soviet Union on Dec. 25, 1991.

"I'm happy that I have lived to see the people waking up. This raises big hopes," the 80-year-old Gorbachev said on Ekho Moskvy radio.

He urged Putin to follow his example and give up power peacefully, saying Putin would be remembered for the positive things he did if he stepped down now. The former Soviet leader, who has grown increasingly critical of Putin, has little influence in Russia today.

But the protesters have no central leader and no candidate capable of posing a serious challenge to Putin, who intends to return to the presidency in a March vote.

Even at Saturday's rally, some of the speakers were jeered by the crowd. The various liberal, nationalist and leftist groups that took part appear united only by their desire to see "Russia without Putin," a popular chant.

Putin, who gave no public response to the protest Saturday, initially derided the demonstrators as paid agents of the West. He also said sarcastically that he thought the white ribbons they wore as an emblem were condoms. Putin has since come to take their protests more seriously, and in an effort to stem the anger he has offered a set of reforms to allow more political competition in future elections.

Kremlin-controlled television covered Saturday's rally, but gave no air time to Putin's harshest critics.

Estimates of the number of demonstrators ranged from the police figure of 30,000 to 120,000 offered by the organizers. Demonstrators packed much of a broad avenue, which has room for nearly 100,000 people, about 2.5 kilometers (some 1.5 miles) from the Kremlin, as the temperature dipped well below freezing.

A stage at the end of the avenue featured banners reading "Russia will be free" and "This election Is a farce." Heavy police cordons encircled the participants, who stood within metal barriers, and a police helicopter hovered overhead.

Alexei Navalny, a corruption-fighting lawyer and popular blogger, electrified the crowd when he took the stage. He soon had the protesters chanting "We are the power!"

Navalny spent 15 days in jail for leading a protest on Dec. 5 that unexpectedly drew more than 5,000 people and set off the chain of demonstrations.

Putin's United Russia party lost 25 percent of its seats in the election, but hung onto a majority in parliament through what independent observers said was widespread fraud. United Russia, seen as representing a corrupt bureaucracy, has become known as the party of crooks and thieves, a phrase coined by Navalny.

"We have enough people here to take the Kremlin," Navalny shouted to the crowd. "But we are peaceful people and we won't do that - yet. But if these crooks and thieves keep cheating us, we will take what is ours."

"We don't trust him," opposition leader Boris Nemtsov told the rally, urging protesters to gather again after the long New Year's holidays to make sure the proposed changes are put into law.

He and other speakers called on the demonstrators to go to the polls in March to unseat Putin. "A thief must not sit in the Kremlin," Nemtsov said.

The protest leaders said they would keep up their push for a rerun of the parliamentary vote and punishment for election officials accused of fraud, while stressing the need to prevent fraud in the March presidential election.

Former world chess champion Garry Kasparov was among those who sought to give the protesters a sense of empowerment.

"There are so many of us here, and they (the government) are few," Kasparov said from the stage. "They are huddled up in fear behind police cordons."

The crowd was largely young, but included a sizable number of middle-aged and elderly people, some of whom limped slowly to the site on walkers and canes.

"We want to back those who are fighting for our rights," said 16-year-old Darya Andryukhina, who said she had also attended the previous rally.

"People have come here because they want respect," said Tamara Voronina, 54, who said she was proud that her three sons also had joined the protest.

Putin's comment about protesters wearing condoms only further infuriated them and inspired some creative responses. One protester Saturday held a picture montage of Putin with his head wrapped in a condom like a grandmother's headscarf. Many inflated condoms along with balloons.

The protests reflect a growing weariness with Putin, who was first elected president in 2000 and remained in charge after moving into the prime minister's seat in 2008. Brazen fraud in the parliamentary vote unexpectedly energized the middle class, which for years had been politically apathetic.

"No one has done more to bring so many people here than Putin, who managed to insult the whole country," said Viktor Shenderovich, a columnist and satirical writer.

Two rallies in St. Petersburg on Saturday drew a total of 4,000 people.

"I'm here because I'm tired of the government's lies," said Dmitry Dervenev, 47, a designer. "The prime minister insulted me personally when he said that people came to the rallies because they were paid by the U.S. State Department. I'm here because I'm a citizen of my country."

Putin accused the United States of encouraging and funding the protests to weaken Russia.

Putin's former finance minister surprised the protesters by saying the current parliament should approve the proposed electoral changes and then step down to allow new parliamentary elections to be held. Alexei Kudrin, who remains close to Putin, warned that the wave of protests could lead to violence and called for establishing a dialogue between the opposition and the government.

"Otherwise we will lose the chance for peaceful transformation," Kudrin said.

Kudrin also joined calls for the ouster of Central Election Commission chief Vladimir Churov.

Putin has promised to liberalize registration rules for opposition parties and restore the direct election of governors he abolished in 2004. Putin's stand-in as president, Dmitry Medvedev, spelled out those and other proposed changes in Thursday's state-of-the nation address.

Gorbachev, however, said the government appears confused.

"They don't know what to do," he said. "They are making attempts to get out of the trap they drove themselves into."